Algebra I Common Core Regents Exam - January 2016, Part 2

High School Math based on the topics required for the Regents
Exam conducted by NYSED. The following are the worked solutions
for the Algebra 1 (Common Core) Regents High School Examination
January 2016.

Algebra I Common Core Regents New York State Exam - January 2016

Algebra 1 - January 2016 Regents - Questions and solutions 21 - 24
21. Which pair of equations could not be used to solve the following
equations for x and y?
4x + 2y = 22
-2x + 2y = -8

22. The graph representing a function is shown below.
Which function has a minimum that is less than the one shown in the
graph?

23. Grisham is considering the three situations below. computations.
I. For the first 28 days, a sunflower grows at a rate of 3.5 cm per day.
II. The value of a car depreciates at a rate of 15% per year after it
is purchased.
III. The amount of bacteria in a culture triples every two days during
an experiment.
Which of the statements describes a situation with an equal difference
over an equal interval?
(1) I, only (3) I and III
(2) II, only (4) II and III

24. After performing analyses on a set of data, Jackie examined the scatter
plot of the residual values for each analysis. Which scatter plot
indicates the best linear fit for the data?

28. The graph below shows the variation in the average temperature of Earth’s surface from 1950–2000,
according to one source.
During which years did the temperature variation change the most per unit time? Explain how you
determined your answer.

Algebra 1 - January 2016 Regents - Questions and solutions 29 - 33
29. The cost of belonging to a gym can be modeled by C(m) = 50m + 79.50, where C(m) is the total
cost for m months of membership.
State the meaning of the slope and y-intercept of this function with respect to the costs associated
with the gym membership.

30. A statistics class surveyed some students during one lunch period to obtain opinions about
television programming preferences. The results of the survey are summarized in the table below.
Based on the sample, predict how many of the school’s 351 males would prefer comedy. Justify
your answer.

31. Given that a > b, solve for x in terms of a and b:
b(x - 3) ≥ ax + 7b

32. Jacob and Jessica are studying the spread of dandelions. Jacob discovers that the growth over
t weeks can be defined by the function f(t) = (8) &bullet; 2t. Jessica finds that the growth function over
t weeks is g(t) = 2t + 3.
Calculate the number of dandelions that Jacob and Jessica will each have after 5 weeks.
Based on the growth from both functions, explain the relationship between f(t) and g(t).

33. Let h(t) = 16t2 + 64t + 80 represent the height of an object above the ground after t seconds.
Determine the number of seconds it takes to achieve its maximum height. Justify your answer.
State the time interval, in seconds, during which the height of the object decreases. Explain your
reasoning.

Algebra 1 - January 2016 Regents - Questions and solutions 34 - 36
34. Fred’s teacher gave the class the quadratic function f(x) = 4x2 + 16x + 9.
a) State two different methods Fred could use to solve the equation f(x) = 0.
b) Using one of the methods stated in part a, solve f(x) = 0 for x, to the nearest tenth.

35. Erica, the manager at Stellarbeans, collected data on the daily high temperature and revenue
from coffee sales. Data from nine days this past fall are shown in the table below.
State the linear regression function, f(t), that estimates the day’s coffee sales with a high
temperature of t. Round all values to the nearest integer.
State the correlation coefficient, r, of the data to the nearest hundredth. Does r indicate a strong
linear relationship between the variables? Explain your reasoning.

36. A contractor has 48 meters of fencing that he is going to use as the perimeter of a rectangular
garden. The length of one side of the garden is represented by x, and the area of the garden is
108 square meters.
Determine, algebraically, the dimensions of the garden in meters.

Algebra 1 - January 2016 Regents - Questions and solutions 37
37. The Reel Good Cinema is conducting a mathematical study. In its theater, there are 200 seats.
Adult tickets cost $12.50 and child tickets cost $6.25. The cinema’s goal is to sell at least $1500
worth of tickets for the theater.
Write a system of linear inequalities that can be used to find the possible combinations of adult
tickets, x, and child tickets, y, that would satisfy the cinema’s goal.
Graph the solution to this system of inequalities on the set of axes on the next page. Label
the solution with an S.
Marta claims that selling 30 adult tickets and 80 child tickets will result in meeting the cinema’s
goal. Explain whether she is correct or incorrect, based on the graph drawn.

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